Process for the rectification of binary liquid mixtures

ABSTRACT

A process for the rectification of binary liquid mixtures is disclosed wherein one component of the mixture is more volatile than the other component. A rectification column is employed having rectification, intermediate and depletion stages, with a working fluid comprised of the components to be separated being employed to furnish energy for the rectification process.

This application is a division of application Ser. No. 290,224, filedAug. 5, 1981, now U.S. Pat. No. 4,411,739.

BACKGROUND OF THE INVENTION

The invention concerns the field of the rectification of liquid mixturesof two components having different boiling points.

The separation by distillation of the components of a binary liquidmixture is a well known and tested method. As a general bibliographicalreference on this subject, for example, the work of S. G. SHINSKEY"Distillation control for production and energy conservation",McGraw-Hill, USA (1977), may be cited and is herein incorporated byreference.

It would certainly be useful to improve conventional rectification forthe purpose of saving energy by trying to obtain better thermodynamicyields.

Rectification columns have already been equipped with heat pumps usingas sources the condensers and the column boilers. These operationsheretofore were limited to applications wherein the boiler temperaturesdid not exceed approximately 80° C., as the result of the temperaturelimitations imposed on the operation of heat pumps presently availableon the market. Even when using working fluids providing higherperformances with boiler temperatures exceeding 80° C. and attaining forexample 120° C., only a small portion of existing columns may be thusequipped. Furthermore, the operations actually realized remain highlyrestricted in numbers, as the economics of their use do not permit rapidrecovery of the investment. The performance of heat pumps (abbreviatedPAC) are inadequate by reason of the limited thermodynamic yield ofconventional materials. In the case under consideration, this yield isaggravated by the exchange temperature deviations due to the use of anintermediate heat transfer fluid between the "condenser-column"-"boiler-PAC" and "column boiler"-"PAC condenser".

The process according to the invention makes it possible both to avoidall temperature limitations and to employ the pumping of heat betweenthe condenser and the boiler of the column with the best thermodynamicyield possible.

The invention takes advantage of a known process designated a"polytropic" process, which is employed in machines designated"polytropic". Such processes and machines are described particularly inFrench applications FR No. 75 114 38 (publication No. 23 07 227), FR No.76 14 965 (publication No. 23 52 247) and FR No. 77 07 041 (publicationNo. 23 83 411), herein incorporated by reference.

Polytropic machines consist of a series of cells with staggeredpressures/temperatures, wherein a working fluid circulates in the formof saturating vapor in contact with its liquid. Furthermore, there is orare present, at least in certain cells, one or several bundles ofheating or cooling tubes, which expose the cells to heat transfer fluidsintroducing the heat of a producing source or extracting heat intendedfor a consuming zone. Finally, each cell is related to its neighbors, onthe one hand, over the path of the vapor, by means of a compressor or aturbine, depending on whether the primary heat entering the process isavailable on the average at a high level of temperature or at a lowlevel, the vapor ascending or descending the levels ofpressures/temperatures thus involving a certain external work which maybe designated the "work of transfer" and on the other hand, over thepath of the liquid circulating in a direction inverse to that of thevapor and in an equal amount, through a calibrated orifice to descendthe levels of pressures/temperatures or by means of a pump to ascend thesaid pressures/temperatures. It will be sufficient for those skilled inthe art to refer to the descriptions of the abovecited patents in orderto recognize the structure and functioning of such machines.

In the case wherein the heat transfer fluid introduces heat (it thencirculates by traversing in series the stages in the direction ofdecreasing temperatures), the vapor of the working fluid is produced bythe boiling of the liquid present in the cell, and, in the contrarycase, the vapor of the working fluid condenses. Thus, the flow rates ofthe vapor and the liquid develop from stage to stage in accordance withthe quantities of heat added or extracted as a function of the Q(T) lawby which the addition or extraction of the heat are effected, i.e. as afunction of the dimensions of the heat transfer bundles.

It is important to note that in principle, at the interface of twosuccessive cells, the sum of the flow rates of the working fluidentering in the form of vapor or in the form of liquid is always equalto the sum of the flow rates of the same working fluid exciting in theform of liquid or the form of vapor, with the flows of the vapor and theliquid of the working fluid circulating in inverse directions within astage alway being equal.

It may be noted that the polytropic machines described in the abovecited patents may be formed by four simple, elementary sequences,namely:

sequence of cooled compressors, used for a process of condensation withthe absorption of work;

sequence of heated compressors, used in a process of boiling with theabsorption of work;

sequence of cooled turbines used in a condensation process with workprovided;

sequence of heated turbines, used in a boiling process with workprovided.

All of these four elementary types of sequences comprise an openterminal stage whereby the liquid and vapor flows of the working fluidenter and exit, and a closed terminal stage wherein the working fluid iseither completely vaporized, or completely condensed.

The table hereinafter indicates the side where the open stage may befound, the entries and exits of the working fluid in regard to thesequence considered, together with the direction of the heat transfefluid.

    ______________________________________                                                                          Direction of                                                                  the heat                                    Type of Sequence                                                                          Open Stage                                                                              Working Fluid                                                                             transfer fluid                              ______________________________________                                        Sequence of heated                                                                        higher    liquid enters,                                                                            decreasing                                  compressors temper-   vapor exits temper-                                                 ature                 atures                                      Sequence of cooled                                                                        lower     vapor enters,                                                                             Increasing                                  compressors temper-   liquid exits                                                                              temper-                                                 atures                atures                                      Sequence of heated                                                                        lower     liquid enters,                                                                            decreasing                                  turbines    temper-   vapor exits temper-                                                 atures                atures                                      Sequence of cooled                                                                        higher    vapor enters,                                                                             Increasing                                  turbines    temper-   liquid exits                                                                              temper-                                                 atures                atures                                      ______________________________________                                    

In these systems, the heat transfer fluid may traverse severalsuccessive stages, or a single stage. In the extreme case, there may bea heat transfer circuit of a different nature per stage of apredetermined sequence.

It is also known that the operation of a polytropic machine may begeneralized in the case wherein the liquid and vapor flow rates of theworking fluid at the inlet of the open stage are different; in thiscase, the difference of the flows circulating in the two directionsremains at a value it has at the inlet until the other terminal stage isreached, which is then traversed by a flow of the working fluid and thusis no longer a closed stage, it is said in such a case that one is inthe presence of a "process open at both ends" or more simply an openprocess.

It is thus noted that the polytropic process that is the most general,has the following characteristics:

(1) It is multiple stage with regard to pressure and temperature.

(2) In each stage, the liquid and the vapor of the condensable workingfluid are in contact and exchange both heat and material.

(3) The vapor of the working liquid circulates from stage to stagetraversing rotating machines, thus involving work. The difference intemperature between two successive stages exists in principle onlybecause of this single fact; the temperature rises from one stage to theother in the direction of the travel of the vapor if the rotatingmachine is a compressor, while it decreases if a turbine is involved.

(4) The liquid of the working fluid circulates from stage to stage inthe direction inverse to the vapor; the liquid and vapor flowscirculating between two stages have a difference which is reflected fromstage to stage.

(5) Each stage may exchange heat with the outside.

The object of the present invention essentially is a process intendedfor the rectification of a binary mixture of two components A and B, Abeing more volatile, without the external addition of heat and providingonly work, the latter being of a value close to the theoretical valuenecessary for the separation of the components A and B (designated thework of separation).

In the most general form, the object of the invention thus is a processfor the rectification of a liquid mixture of two components A and B, Abeing the more volatile, wherein an open polytropic process using acondensable working fluid is utilized, said process comprising aplurality of stages, in each of which the liquid and the vapor of saidworking fluid are present, the flows of the vapor and the liquid of theworking fluid circulating in inverse directions from one stage to theother, the difference berween the liquid and vapor flow rates of theworking fluid circulating between two contiguous stages being conservedfrom stage to stage until the terminal stages; a process wherein, at thelevel of each stage, work and heat exchange with an external heattransfer fluid may be involved, said process being characterized in thatthe mixture of A+B to be rectified is used as the working fluid in theabove-mentioned open polytropic process, said process being designatedthe principal process, with the terminal stage thereof being designated"first stage" and "last stage", so that one travels from the first tothe last stage by following the direction of the travel of the vapor insaid process, and comprising a pressure-temperature distribution suchthat in the first stage there is found only the component B in apractically pure state and in the last stage only a practically pure Acomponent, in that in the stage wherein the liquid concentration isclosest to that of the mixture, the charge to be rectified isintroduced, it being a mixture composed of a flow Δm_(A) of component Aand Δm_(B) of component B, previously brought to thepressure-temperature of said stage, designated the feed stage, thestages proceeding from the increasing direction from the feed stage tothe last stage, being called the rectification stages and constitutingtogether a rectification module, the difference of the vapor and liquidflows of the B component being essentially zero in the rectificationmodule, while the difference of the vapor and liquid flows of the Acomponent is equal to Δm_(A) and is reproduced from stage to stage inthe rectification module to the last stage, where a vapor flow Δm_(A) isrecovered, together with a supplemental vapor flow m_(A) *, by that thesame flow m_(A) * is reinjected, after condensation, in the last stageto constitute the reflux of A, the stages proceeding in the decreasingdirection from the feed stage to the first stage being designated thedepletion stages and constituting together a depletion module, thedifference of the vapor and liquid flows of the component A in thedepletion module being essentially zero, while the difference of thevapor and liquid flows of the component B is equal to Δm_(B) and isreproduced from stag to stage in the depletion mcdule until the firststage, wherein a liquid flow Δm_(B), accompanied by a supplementalliquid flow m_(B) *, is recovered, by that the same flow m_(B) * isreinjected, after vaporization, in the first stage to constitute thereflux of B, with the vapor flow Δm_(A) in the last stage and the liquidflow Δm_(B) in the first stage constituting the production.

BRIEF DESCRIPTION OF THE DRAWINGS

The description hereinafter refers to the drawings attached hereto,wherein:

FIG. 1 is a known equilibrium diagram for binary mixtures;

FIG. 2 is a simplified diagram, similar to that of FIG. 1, demonstratingdifferent variants of the process of the invention;

FIG. 3 is a scheme illustrating the embodiment of the proces of theinvention;

FIG. 4 is an isothermal system for the embodiment of the process of theinvention;

FIG. 5 is a complete device employing the means represented in FIGS. 3and 4;

FIG. 6 is a theoretical scheme illustrating the combination of aprincipal process and an associated process;

FIG. 7 is a more complete scheme employing the means represented in FIG.6;

FIG. 8 is a scheme similar to that of FIG. 7, in a variant ofembodiment;

FIG. 9 illustrates the principal polytropic machine used according tothe invention in the system of FIG. 11;

FIG. 10 illustrates the associated polytropic machine used according tothe invention in the system of FIG. 11;

FIG. 11 is a complete system for the embodiment of a principal processwith pressure and temperature increasing and of an associated turbineprocess;

FIG. 12 illustrates the associated polytropic machine used in the systemof FIG. 13;

FIG. 13 is a complete system for the embodiment of a principal processat a rising pressure and temperature and an associated compressorprocess;

FIG. 14 is a system for the embodiment of a principal process at aconstant pressure and an associated compressor process;

FIG. 15 illustrates the principal polytropic machine used according tothe invention in the system of FIG. 17;

FIG. 16 illustrates the associated polytropic machine used according tothe invention in the system of FIG. 17;

FIG. 17 is a complete system for the embodiment of a principal processat a decreasing pressure and temperature and an associated compressorprocess;

FIG. 18 is a theoretical diagram similar to that of FIGS. 1 and 2 andshowing variants of the invention;

FIG. 19 is a scheme illustrating the process of the invention for theseparation of an azeotropic mixture;

FIG. 20 is a diagram based on FIG. 14 and intended to illustrate thecalculations performed according to the invention;

FIG. 21 illustrates a geometric design to determine the number of stagesof a rectifying column designed in keeping with the invention;

FIGS. 22a and 22b are graphics established for isobutane and propanewith an isobaric principal process;

FIGS. 23a and 23b are graphics established for methanol and water withan isobaric principal process;

FIGS. 24a and 24b are graphic representations established for isobutaneand propane with an isothermal principal process;

FIGS. 25a and 25b are graphic representations established for methanoland water with an isothermal principal process;

FIG. 26 is a diagram illustrating the enthalpic method of calculating aconventional rectification column.

DETAILED DESCRIPTION OF THE INVENTION

In order to illustrate the invention, it is initially convenient torefer to the known pressure-temperature equilibrium curves, which arefunctions of the vapor and liquid concentrations of the A-B mixture.These curves are shown in FIG. 1 for a mixture with a behavior close tothat of ideal solutions; the well known zone curves established for thepressures P₁, P₂, P₃ with P₁ <P₂ <P₃ may be seen therein, where thetemperatures T are represented as functions of the concentrations c ofthe body A, liquid and vapor; the curves (1), (2), (3) of FIG. 1 arerelative to the liquid concentrations, the curves (1'), (2'), (3') arerelative to the vapor concentrations, respectively, for the pressuresp₁, p₂, p₃.

According to a characteristic of the invention, a polytropic machine isoperated with a mixture of the components A, B as the working fluid.

Pressures and temperatures are established in the sequence of stages ofthe machine such as:

    |P.sub.A, T.sub.A |, |P.sub.B, T.sub.B |, . . . |p.sub.i, Ti| . . . |pn, Tn|,

and variable concentration couples of the liquid (x) and the vapor (y),such as:

    |x.sub.A, y.sub.A |, |x.sub.B, y.sub.B |, . . . |Xi, yi| . . . |xn, yn|,

corresponding to an enrichment in one of the components and a depletionin the other component when passing from the first to the last stage.

As an example, with a sequence of heated compressors, in the first andlast the conditions represented in FIG. 1 may be obtained: first stageat p₁, T₁ liquid and vapor concentrations: x₁ and y₁, last stage at p₃T₃, liquid and vapor concentrations: x₃ and y₃.

The theory of polytropic machines further indicates that it is possibleby varying the velocity of the compressors and the distribution of heatadditions at the different stages, to ensure that the conditionsestablished in the first and the last stages yield concentrationscorresponding respectively to pure A and B components.

The conditions of pressure-temperature that are established between thesuccessive stages of polytropic machines thus render it possible toobtain enrichments in A and in B respectively, by turning toward one ofthe other of the ends of the machine, to pass from the pure B componentto the pure A component.

According to the invention, the process is fed with a mixture of Δm_(A)+Δm_(B) designated "the charge", by introducing it in a median stage ofthe polytropic machine and at the ends of said machine, pure flows ofΔm_(A) and pure Δm_(B) are recovered.

Thus, a polytropic machine fed at the level of a stage by a mixtureΔm_(A) +Δm_(B), comprises a combination of three parts:

the feed stage (or intermediate stage);

the rectification module or stage; and

the depletion module or stage.

In these three parts, the vapor and liquid flows circulating between twosuccessive stages having different structures.

In the rectification module, the flows of B vapor and liquid areessentially identical and the difference in the flows of A vapor andliquid amounts to Δm_(A).

In the depletion module, the A flows are essentially identical in thevapor and the liquid; the difference in the flows of the B liquid andvapor amounts to Δm_(B).

The feed stage receives the charge Δm_(A) +Δm_(B), the vapor coming fromthis stage is directed to a terminal stage of the rectification module,in the inverse direction, the liquid entering the feed stage comes fromthe same terminal stage; the structure of these vapor and liquid flowsis that of the rectification module. Similarly, the vapor entering thefeed stage originates in a terminal stage of the depletion module; inthe inverse direction, the liquid flow introduced in the depletionmodule originates in the feed stage; the structure of these vapor andliquid flows is that of the depletion module.

The vapor and liquid effluents are in equilibrium in each stage by meansof direct contact (See FIG. 1) and in view of the pressure-temperatureconditions prevailing in the stage under consideration, the effluentsleaving this stage are in a state corresponding to this equilibrium.There are thus relationships between the flows circulating betweensuccessive stages, the values of Δm_(A) and Δm_(B) and theconcentrations in these stages corresponding to thepressures-temperatures prevailing therein.

In the rectification module, between two successive stages of the orderof i and i+1, the following relationship exists: ##EQU1## wherein M_(A)=vapor flow

Δm_(A) =charge flow in the component A

x_(Ai) +1=concentration of liquid A in the stage i+1

y_(Ai) =vapor concentration of A in the range i.

In the depletion module between two successive stages of rank j and j+1,the following relationships prevail: ##EQU2## wherein M_(B) =liquid flow

Δm_(B) =flow of charge in the component B

x_(Bj) +1=liquid concentration of B in the stage of rank j+1.

y_(Bj) =vapor concentration of B in the stage of rank j.

By applying the two relations (a) and (b) at the level of the feedstage, on the side of the depletion module and the side of the feedmodule, it is seen that the concentration established in said feed stageis the same as in the charge.

By applying the relations (a) and (b) to the rectification module at thelevel of the terminal stage noncontiguous with the feed stage anddesignated the "last stage", it is seen that there issues from saidstage a flow M_(A) * of the vapor of A, so that M_(A) *>Δm_(A), with thedifference M_(A) *-Δm_(A) constituting a supplemental flow which, inkeeping with the rules of the operation of polytropic machines, shouldbe reintroduced in the vapor state in the same stage; this flow isdesignated "reflux of A".

By applying the relations (a) and (b) to the depletion module at thelevel of the terminal stage noncontiguous with the feed stage anddesignated the "first stage", it is seen that there issues from thestage a flow M_(B) * of the vapor of B, so that M_(B) *>Δm_(B), with thedifference M_(B) *-Δm_(B) constituting a supplemental flow which, inkeeping with the rules of the operation of polytropic machines, shouldbe reintroduced in the vapor state in the same stage; this flow isdesignated "reflux of B".

According to the characteristic complementary dispositions of theprocess according to the invention, the process of separation iscombined with three other processes with which it exchanges heat in theform of the latent heat of the component A.

The first of these processes, designated associated processes, has asits object the exchange of heat with the binary fluid (A, B) in thedifferent stages of the separation process, so that the heat istransferred to the vaporizing binary fluid, by the condensing A vaporand that it is removed from the binary fluid during condensation to besupplied to the vaporizing liquid A component.

According to the invention, the heat for the exchanges is supplied bythe flow of the vapor A escaping from the last stage of the separationprocess, said vapor carrying the latent heat of a flow comprising boththe production Δm_(A) and the reflux of A. The heat requirement of theseparation process is equal to the heat of evaporation of the"production flow Δm_(A) and the reflux of A", reduced by the heat ofcondensation of the reflux vapor of B; the total addition of heat in theseparation process is thus in excess, with respect to the requirements,by a quantity equal to the heat of condensation of the reflux of Bincreased by the work applied to the system and the thermodynamicirreversibilities; it is seen therefore that the flow of A exiting fromthe associated process still carries this excess heat in the form of thelatent heat of its vapor.

The flow of A is then introduced in the second process which is a boilerprocess of the supplemental liquid flow of B, the vapor of B produced inthis manner constitutes the flow of the reflux vapor of B.

The exiting flow of A again carries a latent heat slightly higher thanthe work supplied to the system; it is thus necessary to condense a flowof the vapor of A in a third process, designated the condensationprocess of A and evacuating the excess heat to the outside. According tothe invention, the process is interposed in the vapor circuit of Aconnected with the terminal process at a lower temperature level of theassociated process.

According to the complementary characteristics of the process of theinvention, measures are taken so that the exchanges describedhereinabove are effected in conditions that are as close as possible toreversibility. The description hereinafter, with reference to FIG. 2,illustrates these characteristics.

FIG. 2 is a diagram similar to that of FIG. 1, wherein the vapor andliquid concentrations are represented at equilibrium as functions ofpressure and temperature; this diagram makes it possible to demonstratethe representative paths of evolution possible in the successive stagesof a separation process. The representative point of the first stage ofthis process is always the point Z; the points Z₁, Z₂, . . . etc. Z₅ arerepresentative of the last stage; the path ZZ₁ is at an increasingpressure and is isothermal; the path ZZ₂ is at increasing pressure andan increasing temperature; the path ZZ₃ is at increasing pressure anddecreasing temperature; the path ZZ₄ is at constant pressure and adeclining temperature. The path ZZ₅ is at a decreasing pressure andtemperature.

The characteristic dispositions of the process according to theinvention are applicable to all cases.

In the path ZZ₁, the separation process is isothermal; the exchangesbetween the binary fluid and the componant A are effected in theexchangers; the deviation of the exchange temperature between the vaporof A and the binary fluid is obtained by compressing said vapor of Aprior to its introduction of the exchangers; the temperature differenceto be established between the liquid A and the binary fluid is obtainedby means of a "flash" expansion of the condensate of A.

In FIG. 3, an illustrative system for the embodiment of the process ofthe invention in the case of the isothermal path ZZ₁ is shown. In such aprocess, the entirety of the stages is essentially at the sametemperature. It is seen in FIG. 3 that the system comprises essentiallya depletion module 10, a rectification module 11 and a stage 12 of theintroduction of the mixture Δm_(A) +Δm_(B).

The introductory stage 12 is related to the rectification module bymeans of tubes 13 (vapor) and 14 (liquid) and to the depletion module 10by means of the tubes 15 (vapor) and 16 (liquid).

In the rectification module 11, the vapor of B is progressivelycondensed so that only an essentially pure component A remains, both inthe vapor and the liquid at the level of the last stage; the enrichmentof the mixture (both vapor and liquid) results equally from thevaporization of A; if in a stage the heat produced by the condensationof B is carried over to the vaporization of A, the stage is exothermic;in the rectification module 11, certain stages may be exothermic inprinciple, the others being endothermic; in practice, the rectificationmodule 11 is almost always exothermic in all of its stages. From thelast stage (index n) of the module 11, there issues at 17 a flow M_(A) *of the pure A componant in the vapor state, with M_(A) *=Δm_(A) +m_(An),m_(An) being the supplemental flow introduced into the same stage in theliquid state at 18.

In the depletion module 10, the titer of the componant B, both liquidand vapor, increases constantly when moving from the stage 12 of theintroduction toward the first stage. At the level of the first stage, aflow M_(B) * of the pure component B exits, in 19 with M_(B) *=m_(B1)+Δm_(B), m_(B1) being the supplemental flow introduced in the vaporstate at 20. In all of the stages of the module 10, A and B are beingvaporized simultaneously. Thus, the depletion module 10 is endothermicat the level of all of its stages. It is evident that when one speaks inthe present description of an essentially pure component A, saidcomponent A is in a state of controlled purity, which may attain themaximum purity attainable in an industrial operation.

In FIG. 4, an isothermal system of the type illustrated schematically inFIG. 3, is shown, it comprises means to condense the flow M_(An), meansto vaporize the flow m_(B1), together with means to maintain the modules10 and 11 at a constant temperature.

Let us suppose, in a nonlimiting manner, that the rectification module11 is exothermic; the depletion module 10 is always endothermic. Thecases wherein the module 11 is entirely or partly endothermic is part ofgeneral knowledge and is within the range of those skilled in the art.

In FIG. 4, similar elements or means are designated by the same signs orcodes of reference as in FIG. 3.

The flow M_(A) * exiting at 17 from the rectification module 11 iscompressed in at least one compressor 21 prior to its introduction at 23through the line 22 in the depletion module 10. The temperature of thecondensation of the vapor M_(A) * rises, thereby generating the exchangeΔT. The flow then traverses the module 10 (path 23-24), while partiallycondensing; measures are taken at the level of the exchangers(condensers of A, boiler of the mixture A, B) to maintain thetemperature deviation ΔT essentially constant; the depletion module 10is thus mostly at a constant temperature. The two-phase mixture of Asubsequently arrives in an area 29, where the vapor and liquid areseparated.

On its part, the liquid flow M_(B) * exiting at 19 from the module 10 isseparated into two parts:

the flow Δm_(B), which is collected in the line 25 and which constitutesthe production of B;

the flow m_(B1) which is transported through the conduit 26 and which ismade to traverse the exchanger 27. After passing through the exchanger27, the flow m_(B1), in the form of vapor, is reintroduced in the module10 at 20. The exchange fluid in the exchanger 27 is the vapor of A. Theexchanger 27 is thus a condenser of A and a boiler of B. For thispurpose, the vapor of A coming from the area 29 is transported throughthe line 29a, traverses the exchanger 27 and then circulates in the line31.

The flow m_(B1) is evaporated in its entirety in the course of itspassage through the exchanger 27, prior to being introduced through theline 28, in the form of vapor in the first stage of the module 10 at 20.

The flow of A coming from the exchanger 27 through the line 31, is notcompletely condensed; it is then passed into the atmospheric condenser30, from which it emerges completely liquid. It is transported in theconduit 32 to be introduced in the area 29, which is the general reserveof liquid A at the isothermal operating temperature of the system.

From the reserve 29, a liquid flow is extracted, a part m_(An) of whichis returned through the tubing 33, 34 to 18 in the rectification module11, while the other part passes through the tubing 33, 35, whiletraversing a laminar flash valve 36, which has the purpose of droppingits temperature of ΔT' below the temperature of the system, therebycreating the temperature difference of the exchange. The flow of Atraverses the rectification module 11 at y, while taking up the heat andbecoming vaporized; the vapor of A produced in 37 is then compressed in38 to be combined through the line 39 the vapor circuit effected by theline 22.

As an illustration, in FIG. 5 a device using the means shown in FIG. 3and 4 is shown. In the example chosen, the depletion module 11 comprisestwo stages or cells 50, 51 and the rectification module 10 comprisesthree stages or cells 52, 53, 54. The introduction stage is designatedby the reference 12, as in FIGS. 3 and 4.

In the module 11, the exchange cells 50 and 51 are connected by a tube55 with the throttling flash valve 56. Between the stage 12 and stage 51there is also provided valve 57 in the tube 16. Similarly, between thestages of the rectification module 10, throttling means (valves) areprovided in the path of the vapor, respectively 58 in the tube 14between stage 12 and stage 52, a valve 59 between the stages 52 and 53and a valve 60 between the stages 53 and 54. In a known manner,compressors are associated with the different stages. Thus, a compressor61 is provided between the stages 50 and 51, a compressor 62 between thestages 51 and 52, a compressor 63 between the stages 12 and 52, acompressor 64 between the stages 52 and 53 and a compressor 65 betweenthe stages 53 and 54. The paths of the vapors between the differentstages and the corresponding compressors are indicated by the fine linesand by the arrows.

The compressor 21 is provided at the outlet 17 of the module 10 asalready shown in FIGS. 3 and 4.

The paths of the liquid are shown by bold lines.

The exchange circuits in the stages 50 and 51 of the module 11 aredesignated respectively by the references 66 and 67. The exchangecircuits in the stages 52, 53 and 54 of the module 10 are designatedrespecttively by the references 68, 69 and 70.

The same elements as in FIGS. 3 and 4 are found in FIG. 5, designated bythe same references. There is, therefore, no need to describe themagain, their function having been already illustrated. An additionalbuffer reservoir 71 is further shown, mounted on the line 35 and feedingthe last stage of the module 11. FIG. 5 corresponds to an actualembodiment of an isothermal system operating according to thetheoretical curve ZZ₁ of the graphical representation of FIG. 2.

For non-isothermal polytropic systems, the process of separation takesplace a staggered temperatures. The assembly diagram of the system isidentical with that of FIG. 3, but in this case the successive statesencountered by moving from the first stage toward the last onecorrespond on the diagram of FIG. 2 (liquid-vapor equilibrium diagram)to the paths ZZ₂, ZZ₃, ZZ₄ and ZZ₅. The paths are shown in FIG. 2 byfollowing the liquid states, but it is obvious to those skilled in theart that the vapor state may be derived at any point read on the path,from the homologous curve representing the vapor state at the sametemperature.

On all of the paths other than the isothermal path ZZ₁, the separationprocess takes place at staggered temperatures. The associated process isa polytropic process comprising the same number of processes as theseparation process, the stages of the same rank being homologous in thetwo processes, which the stages designated "first" and "last" of theassociated process being homologues of the stage of the same name of theseparation process and each stage of rank i exchanging heat at atemperature Ti with its homologue of the associated process at atemperature T'_(i), the temperature difference T_(i) -T'_(i) beingpositive when the behavoir of binary fluid exchange is condensing andnegative if it is boiling.

It will now be shown how the different characteristics define theoperation of the systems by means of the different paths of FIG. 2,other than the isothermal path ZZ₁.

It will now be shown by what means M_(A) * is condensed, M_(B1) isevaporated and how the successive temperatures of the stages aremaintained at the values specified by the paths envisioned. Thedescription hereinafter is prepared, for the sake of simplicity, for thecase of an ideal machine.

As mentioned hereinabove, the system according to the invention consistsessentially of the association of the polytropic separation process,designated the principal process, with another polytropic processoperating with the component A as the working fluid, to be designatedthe associated process. The associated process comprises the same numberof stages as the principal process; the successive stages of the twoprocesses being homologous in the association considered, with twohomologous stages exchanging heat so as to be at the same temperature(or at least to maintain at an adequate value their temperaturedifference, which is the deviation of the exchange temperature).

FIG. 6 is a theoretical scheme illustrating the combination, accordingto the invention, of a principal process and an associated process. Theprincipal process is illustrated by the block 100, with itsrectification module 110, its depletion module 111 and its stage 112 forthe introduction of the charge Δm_(A) +Δm_(B).

The associated process is represented by the block 200. As seen in FIG.3, the principal process 100 provides at 117 (last stage of therectification module) a flow M_(A) * of vapor, with M_(A) *=m_(An)+Δm_(A), while the flow m_(An) is reintroduced at 118. A liquid flowM_(B) * further exits from the first stage of the depletion module at119 and a (vapor) flow m_(B1) is introduced at 120. According to theinvention, the flow M_(A) * exiting at 117 of the process 100 isintroduced at 201 into the associated process 200. This same process isto restitute at 202 a liquid flow equal to m_(An), this flow then beingtransported through the conduit 203 to be introduced at 118. Thedifference in the vapor and liquid flows at the ends 201, 202 of theprocess 200 may be written as M_(A) *-m_(An) =Δm_(An).

At the other end of the process 200, at 204 a vapor flow m_(A1) +Δm_(A)exits and at 205 a liquid flow m_(A1) enters. For the sake of clarity,in FIG. 6 only the circulation of the fluid A is shown. Similarly, thecorrespondence between the respective stages of the principal process110 and the associated process 200 is indicated schematically by thearrows f₁, f₂ . . . f_(n), with the correspondence of the temperaturelevels at each stage being illustrated by the temperatures θ₁ ←→θ₁ ', θ₂←→θ₂ ' . . . θ_(n) ←→θ_(n) '.

In FIG. 7 the schematic representation of the Figure is completed byadding the liquid B and other elements necessary for the heat exchangesin the system. At the left side of FIG. 7 there is seen an exchanger 127wherein the component A coming from the outlet 204 of the associatedprocess 200 through the line 180 is circulating on the one hand, and onthe other some of the component B coming from the outlet 119 of theprincipal process 100, through the line 126. The component A traversesthe exchanger 127 while condensing partially and is recovered in theconduit 131. The quantity m_(B1) of the component B passing through theexchanger 127 evaporate totally therein and exits by the line 128 to beintroduced in the principal process at 120.

Further, an atmospheric condenser 130 is seen, wherein the two-phaseflow of the component A is transported by the conduit 131, said flowexiting from the exchanger 127. The vapor of component A condensescompletely therein. In the outlet conduit 132, there is recovered on theone hand the production Δm_(A) of the component A (line 181) and on theother, the flow m_(A1), which is reintroduced through the conduit 182 atthe inlet 205 of the associated process 200. The arrow Q' indicates theheat rejection of the system. The production Δm_(B) is recovered in theline 125.

The dispositions described with reference to FIG. 7 are suitable if inthe principal process 100, the temperature θ₁ in the first stage is lessthan θ_(n) of the last stage, i.e. if the process 100 is at a risingtemperature: the reject heat Q' is evacuated into the atmosphere at thelowest temperature of the process. In the contrary case, i.e. when thelow level temperature is at the side of the last stage of the process200, the disposition shown in FIG. 8 must be adopted.

The elements common to FIGS. 7 and 8 carry the same reference symbols.It is seen in FIG. 8 that the component A (vapor flow m_(A1)) comingfrom the outlet 204 of the associated process 200 passes through theconduit 180, traverses the exchanger 127 and is recycled (liquid flowm_(A1)) to the inlet 205 of the same process 200. The fluid B of theexchange is, as in FIG. 7, taken at the outlet 119 (flow M*_(B)) of theprincipal process 100, passes, following the removal of the productionΔm_(B) of B in the conduit 125, into the conduit 126 and traverses theexchanger 127 while evaporating completely, to be returned (vapor flowm_(B1)) through the line 128 to the inlet 120 of the process 100.

The atmospheric condenser 130, located at the right side of the drawingin FIG. 8, receives through the conduit 185 the total flow of A, orM*_(A) =m_(An) +Δm_(A), coming at 117 of the principal process 100. Atthe outlet of the condenser 130, at 181 the production Δm_(A) of A isrecovered and a flow m_(An) is returned through the conduit 186 to theend 201 of the associated process 200.

The systems corresponding in a precise manner to the paths ZZ₂, ZZ₃,ZZ₄, and ZZ₅ shall now be desscribed and illustrated (FIG. 2). Briefly,these path correspond to the following situations for a polytropicseparation machine using the principal polytropic process:

path ZZ₂ =machine with compressors, cooled at rising temperatures;

path ZZ₃ =machine with compressors, heated, at decreasing temperatures;

path ZZ₄ =isobaric machine (case of the conventional distillationcolumn), at decreasing temperatures;

path ZZ₅ =machine with turbines, heated, at decreasing temperatures.

The systems corresponding to these different paths shall be describedseparately.

PATH ZZ₂

The principal process is at pressures and temperatures rising from thefirst to the last stage; the associated process is a turbine process;the process of th condensation of A is interposed in the vapor circuitof A exiting from the first stage of the associated process, in serieswith the boiling process of B; the flow of A exiting from the twoprocesses is liquid and the production Δm_(A) of A may be taken fromthem; the rest is returned to the first stage of the associated process.The difference between the vapor flow of A coming from the first stageof the associated process and the liquid flow of A entering therein isthus Δm_(A) ; according to the polytropic invention, this difference iswell maintained to the last stage of said process. In effect, the latterreceives the entirety of the flow coming from the separation process andevacuates only the supplemental flow (m_(A)) of the liquid component A.The difference thus is Δm_(A), which is the production of A.

In order to facilitate the representation, in FIG. 9 the principalpolytropic machine operating according to the invention with the mixtureA+B as the working fluid, is shown; in FIG. 10 the associated polytropicmachine, operating with the fluid A alone as the working fluid is shown;and in FIG. 11 the combination of these two machines, which is thepolytropic system effecting the process of type ZZ₂, is shown.

It is not necessary to describe in detail the machine of FIG. 9, whichis of the general type conforming to the schematic representation ofFIG. 3. Concerning the configuration proper of such a machine, a personskilled in the art might want to refer to the patents mentioned in theintroduction of the present description, should this be necessary. Themachine is of the compressor sequence type, cooled, and thus comprises acertain number of stages or cells of exchange, E₁, E₂, . . . E_(i) . . .E_(n), communicating with each other both in the liquid and the vaporphase. The working fluid is the binary mixture A+B. Temperatures and thepressure are rising from the first stage E₁ to the last sta E_(n). Thecompressors K₁, K₂ . . . K_(i) . . . K_(n) are connected to each stageas shown in FIG. 9 and the vapor flow of the binary mixture A+Bcirculates in this series of compressors. The individual liquid flowspass from stage to stage with the interposition of a flash throttlevalve V₁, V₂ . . . V_(n-1).

At F_(l), F₂, . . . F_(i) . . . F_(n), the exchange bundles are shownschematically; according to the invention, they belong to the associatemachine (FIG. 10).

Overall, a vapor flow equal to m_(B1) of the fluid B enters into thecompressor K₁ of the first E₁. From the first stage E₁ a liquid flowM*_(B) of the fluid B exists, with M*_(B) =m_(B1) +Δm_(B), has beenexplained hereinabove.

At the level of the last stage E_(n), a vapor flow of the component Aequal to M*_(A), with M*_(A) =m_(An) +Δm_(A), leaves the compressorK_(n) and A in the liquid state, a flow m_(An) enters.

In FIG. 10, an associated polytropic machine which is part of a sequenceof cooled turbines, is represented schematically. It comprises a seriesof stages E'₁, E'₂ . . . E'_(n) with their corresponding turbines T₁, T₂. . . T_(i) . . . T_(n). The vapor flow of the component A passessuccessively into the turbines while being cooled, the flow M*_(A) beingintroduced in the vapor stage into the last turbine T_(n). Each stagealso communicates with the adjacent stages by means of the liquid phaseof the component A, as shown schematically by the circuits comprisingthe throttle flash valves V'₁, V'₂ . . . V'_(i) . . . V'_(n-1). A liquidflow equal to m_(A1) enters the first stage E'₁ and from the last stagea liquid flow m_(An) issues. A total flow of m_(A1) +Δm_(A) is recoveredat the outlet of the first stage.

According to the invention, the polytropic machines of FIGS. 9 and 10are associated as shown in FIG. 11.

To each stage E₁, E₂ . . . E_(i) . . . E_(n) of the polytropic machineworking with compressors and the binary fluid, a stage E'₁, E'₂ . . .E'_(i) . . . E'_(n) of the polytropic machine with turbines corresponds,the latter having the component A as its working fluid.

The effluent of the first turbine is transported through the conduit 380and an exchanger 327, which has the same function as the exchange 127 ofFIG. 7. At the outlet of the exchanger 327, the fluid A, partiallycondensed, passes into the conduit 331 and then into the atmosphericcondenser 330, which has the same function as the condenser 130 in FIG.7. At the outlet of the condenser 330, the production μm_(A) isrecovered in the conduit 381 and a flow m_(A1) is introduced through theconduit 382 in the first stage E'₁. Further, the flow of the component Bissuing from the first stage E₁ is in part conducted in 325 to furnishthe production Δm_(B) and the rest is passed through the conduit 326into the exchanger 327, where it vaporizes completely prior to beingintroduced through the conduit 328 into the first stage E₁.

At the level of the last stages E_(n), E'_(n), the flow m_(An) of theliquid coming from E'_(n) is introduced at 318 into E_(n) and the vaporflow M*_(A) coming from E_(n) at 317, is conducted to the compressorK_(n).

PATH ZZ₃

The principal process is always at rising pressures from the first tothe last stage, but in this instance with the temperature decreasing;the associated process here is a compressor process; the condensationprocess of A receives a vapor flow m'_(A), carrying the heat rejected bythe system, coming from the last stage of the separation process; theproduction m_(A) is extracted from the liquid flow coming from thecondensation process of A, the rest, m'_(A) -Δm_(A), is returned to thelast stage of the separation process; in its turn, the last stage of theassociated process has received the vapor flow of A equal to m_(A)+Δm_(A) -m'_(A) ; the difference between the vapor and liquid flows ofA, which is zero at the first stage, is maintained and from the laststage of the associated process a liquid flow A issues, hich is alsoequal to m_(A) +Δm_(A) -m'_(A) ; this flow is conducted to the laststage of the separation process, which receives all of the liquid flowm_(A).

In FIG. 12, the diagram of the associated process and in FIG. 13, thepolytropic system corresponding to the past ZZ₃, are shown. Theprincipal process, which operates with the A+B mixture as the workingfluid, is the one shown in FIG. 9. The details of these machines, whichare identical with those described hereinabove, will not be repeatedhere (FIGS. 9 to 11). In all of these drawings, the same references havebeen used to indicate the elements. It is sufficient for those skilledin the art to see the inputs and outputs of the fluids.

Thus, in FIG. 12, the compressors K'₁, K'₂ . . . K'_(i) . . . K'_(n) areseen in succession; they correspond respectively to the stages E'₁, E'₂. . . E'_(i) . . . E'_(n). At the level of the first stage E'₁, a flowof the liquid component A equal to m_(A1) enters and a vapor flow equalto m_(A1) +Δm_(A) exits. At the level of the last stage, from E'_(n) aflow m_(An) of the liquid exits and the compressor K'_(n) is fed by avapor flow m_(An) +Δm_(A) orM*_(A).

FIG. 13 represents a system according to the invention. A polytropicmachine of the principal process is seen; it comprises the stages E₁, E₂. . . E_(i) . . . E_(n) with the compressors K₁, K₂ . . . K_(i) . . .K_(n) and the machine of FIG. 12, which is associated with therespective stages of E'₁, E'₂ . . . E_(i) . . . E_(n), with the sequenceof the compressors K'₁, K'₂ . . . K'_(i) . . . K'_(n). FIG. 13 alsoshows the exchanger 427 and the atmospheric condenser 430. Theconnections between these elements are shown in the drawings and thelatter is an integral part of the description. The inlets and outlets ofthe fluid are also illustrated in the drawing.

PATH ZZ₄

The principal process is at a constant pressure; the associated processis a compressor process; the condensation process of A receives a vaporflow m'_(A), carrying the reject heat of the system, coming from thelast stage of the separation process; the production m_(A) is extractedfrom the liquid flow coming from the condensation process of A, therest, i.e. m'_(A) -Δm_(A), is returned to the last stage of theseparation process, while in its turn, the last stage of the associatedprocess has received the vapor flow of A equal to m_(A) +Δm_(A) -m'_(A); the difference of the vapor and liquid flows of A, which is zero inthe first stage, is maintained, and from the first stage of theassociated process there issues a liquid flow of A which is also equalto m_(A) +Δm'_(A) ; this flow is conducted to the last stage of theseparation process; the latter thus receives all of the liquid flowm_(A).

The system to effect such a process is shown in FIG. 14. The principalpolytropic machine is shown in the form of a distillation column 500with its stages or plates E₁, E₂ . . . E_(i) . . . E_(n). The associatedmachine is a sequence of compressors, compressing the stages E'₁, E'₂ .. . E'_(i) . . . E'_(n), with the compressors K'₁, K'₂ . . . K'_(i) . .. K'_(n). The exchanger 527 and the atmospheric condenser 530 are alsoshown. The drawing clearly shows the inlets, outlets and the circulationof the fluids and it is a integral part of the present description.

PATH ZZ₅

The principal process is at decreasing pressures and temperatures, it isa turbine process; the associated process is a compressor process; thecondensation process of A receives a vapor flow m'_(A), carrying theheat rejected by the system, coming from the last stage of the"separation" process; the production Δm_(A) is extracted from the liquidflow issuing from the condensation process of A, the rest, i.e. m'_(A)-Δm_(A), is returned to the last stage of the separation process; in itsturn, the last stage of the associated process has received the vaporflow of A equal to m_(A) +Δm_(A) -m'_(A) ; the difference of the vaporand liquid flows of A, which is zero at the first stage, is maintained,and from the last stage of the associated process a liquid flow of Aissues, which also is equal to m_(A) +Δm_(A) -m'_(A) ; this flow isconducted to the last stage of the process of separation; the lattertherefore receives the entirety of the liquid flow m_(A).

FIGS. 15 to 17 illustrate such a system.

FIG. 15 shows schematically the principal polytropic machine with itsstages E₁, E₂ . . . E_(i) . . . E_(n) and the corresponding turbines T₁,T₂ . . . T_(i) . . . T_(n).

FIG. 16 shows schematically the associate machine which consists of aseries of compressors operating with the A component as the workingfluid. The stages E'₁, E'₂ . . . E'_(i) . . . E'_(n) with thecorresponding compressors K'₁, K'₂ . . . K'_(i) . . . K'_(n), are seen.A condenser 550 is also provided, it receives the vapor flow m_(A1)coming from the first compressor K'₁ and condenses it completely to formthe liquid to be introduced in the first stage E'₁.

FIG. 17 represents the combination, according to the invention, of themachines shown individually in FIG. 15 and 16. The stages E₁, E₂, . . .E_(i) . . . E_(n) are seen with their turbines T₁, T₂ . . . T_(i) . . .T_(n), which are associated respectively with the stages E'₁, E'₂ . . .E'_(i) . . . E'_(n) with their compressors K'₁, K'₂ . . . K'_(i) . . .K'_(n). There is also seen the exchanger 627 and the atmosphericcondenser 630, the functions whereof have been described hereinabove.The inlets, outlets and circulations of the fluids are seen clearly inFIG. 17, which is an integral part of the present description.

The paths ZZ₁ (isothermal), ZZ₂, ZZ₃, ZZ₄ (isobaric) and ZZ₅ are themost common in actual practice. However, the invention concerns alsomore complex processes, the representative paths whereof may comprisemaxima, minima or broken lines. Such complex paths may be separated intothe individual processes as described hereinabove.

It is also obvious that the discussion presented in the foregoing iswith reference to ideal machines operating without loss, in order tofacilitate the presentation. In actual practice such losses must betaken into consideration, as it is well known to those skilled in theart.

The invention provides a process employing only reversible operations,at least when reference is made to an ideal process only. Application ofthe first law of thermodynamics to the overall system shows that thework W introduced in equal to the heat rejected Q, Q=W.

This work represents the minimum work of separation.

The application of the second law of thermodynamics, with the assumptionto be rigorous that the separated products Δm_(A) and Δm_(B) are heatedto the temperature of the introduction of the mixture by interchangewith the process, so that thereis no appreciable flow of heat across theprocess, results in the fact that there is no flow of entropy throughthe entirety of the system, because the process is by assumption,reversible. The following relation may thus be written:

    ΔS.sub.mel -ΔS.sub.therm =0

wherein ΔS_(mel) is the entropy of the sample mixture Δm_(A) +Δm_(B),and ΔS_(ther) is such that Q=T₀ ×ΔS_(ther) with T₀ =the low leveltemperature of the process.

Therefore:

    W=T.sub.0 ×ΔS.sub.mel.

ΔS_(mel) being a value attached to the product to be separated, theabove relation indicates that the works of the above described processesdiffer among themselves by the temperature of rejection T₀.

All of the above presented considerations apply to the cases wherein theliquid-vapor equilibrium curves are those of mixtures essentiallyobeying the laws of ideal solutions; these are families of curvessimilar to those in FIG. 1. For example, when one is moving on thediagram from Z to Z₁ (FIG. 2), the pressure is rising.

When, as shown in FIG. 18, the equilibrium curves present a minimum,such as Z' (the case of an azeotropic mixture), the path Z₀ Z'₁comprises two parts.

Path Z₀ Z' remains at rising pressures.

Path Z'Z'₁ is at decreasing pressures.

The system to effect such a process, resulting from the combination oftwo individual processes, may consist of a first process with a seriesof compressors, such as those shown in FIG. 9, and a second process witha series of turbines, such as those shown in FIG. 15, the two processesoperating with the binary mixture A+B as the working fluid.

The point of introduction of the mixture may be located anywhere inrelation to the point of bridging of the two processes. For example, itmay be located (FIG. 19) in the series of compressors.

FIG. 19 is a schematic example of the machine operating according to thepath Z₀ Z'Z'₁. The first process, with the series of compressors, isrepresented by the block 700 and the second, with the series ofturbines, by the block 701. The joining interface of the two processesis illustrated by the line X-Y. The mixture of m_(A) +m_(B) isintroduced at the stage E_(i) of the process 700. Overall, the depletionmodule is represented by 702 and the rectification module by 703.

In order to render the operation of the system stable, a cleardiscontinuity of concentrations may be created in A, between the laststage of the process 700 and the first stage of the process 701, byinjecting in the latter a small flow of the pure component A.

It is obvious that the invention is not limited by the precedingdescription and that numerous variants may be effected without exceedingthe scope of the invention. Polytropic processes were illustrated byexamples. But the invention concerns polytropic processes for therectification of the greatest variety of binary mixtures, such as themixtures of water and liquid organic compounds, for example methanol andmixtures of hydrocarbons.

Practical Application of an Isobaric Process

In the description to follow hereinafter, the practical application of asystem of the type shown in FIG. 14, i.e. an isobaric process, isillustrated. To facilitate the description, FIG. 14 is shown in anotherform and the system is demonstrated in FIG. 20. In the figure, side byside the rectification column (principal process) and the associatedprocess (PAC) are shown. The column and the PAC are graduated from topto bottom; two points at the same heights are at the same temperature.The drawing of FIG. 20 is an integral part of the present descriptionand therein are found the fluid circulations and the characterization ofthe above described thermodynamic values. All of these notions arereadily accessible to those skilled in the art and do not requirecomplementary development.

In order to make the operation correspond completely to the idealscheme, the pure, liquid components A and B exit at temperature T* atwhich they have entered the state of mixture.

In the drawing the vapor flows are designated by the exponent v and theliquid flows by the exponent l. On top of the column, the vapor flow ofA, or m_(A) +Δm_(A), is withdrawn. The flow δm_(A) if the one with itslatent heat corresponding to the reject heat. It must therefore becondensed at the top of the column. Calculations are thereby simplified.The result is the general organization of flows appearing in FIG. 20.

The relationship expressing that the entropy flux across the column iszero (because its operation is reversible) may be written as: ##EQU3##

The following relationship is obtained by applying the second law ofthermodynamics (1): ##EQU4## wherein ΔS* is the entropy flux of themixture,

ΔS_(th) is the entropy flux originating in reversible exchanges of heat.

According to the first law of thermodynamics, the enthalpy balance overthe column is expressed by the following relationship (2):

    |m.sup.(+).sub.A +Δm.sub.A |L.sub.A (T)-δm.sub.A C.sub.1A (T*-T)-m.sub.B L.sub.B (T')+Q.sub.1 =0 (2)

For the PAC, the second law is expressed by the relationship (3):##EQU5##

The first law, written for the PAC, reads:

    -|m.sub.A.sup.(T) +δm.sub.A |L.sub.A (T)+M'.sub.A L.sub.A (T)+δm.sub.A C.sub.1A |T*-T'|-Q.sub.1 -W=0 (4)

By combining the relations (1) and (3) on the one hand and (2) and (4)on the other, the following two equations are obtained:

    W=|Δm.sub.A -δm.sub.A |L.sub.A (T)=TΔS*

Finally, the heats exchanged in the condenser follow the followingequation:

    M'.sub.A L.sub.A (T')=m.sub.B L.sub.B (T')

Since the relations of the concentrations at equilibrium (xA(T), yA(T),etc. . . . ) as a function of T are known, the following may be derived:

in the rectification module: ##EQU6## in the depletion module: ##EQU7##

The entirety of the equations presented hereinabove thus make itpossible to determine the work of separation, i.e. the work required toseparate the components A and B of the mixture, when using the means ofthe invention.

Still within the application of an isobaric process, actual indicationsof the calculation of the number of stages in the column, in view of apractical application, will now be given.

In FIG. 21, a geometric design facilitating such a determination, isshown. Initially, the abovementioned equation (a) should be recalled; itis applicable to the rectification module between two successive stagesof the order of i and i+1. ##EQU8##

This equation may also be written as ##EQU9##

As shown by the diagram in FIG. 21, the construction of the point i+1from the point i is as follows:

a horizontal line is drawn through i to determine the point A,

the length, freely chosen, of ##EQU10## is marked off, A and B areconnected to determine the point C from which one ascends to i+1.

Means to determine graphically the ratio of ##EQU11## mini that would beobtained with an infinite number of plates, are derived.

Beginning with ##EQU12## mini, the actual ##EQU13## may be determined,for example by writing: ##EQU14##

By maintaining K constant in the construction of i+1 as a closer andcloser function of i, it is possible by means of several successiveconstructions, to establish a relationship between K and the number ofplates. The useful number of plates may thus be determined.

In the depletion module, the following relationship is valid: ##EQU15##

The same expression as before is thus obtained.

To construct the points representative of the successive stages, thesame method is used, but with ##EQU16##

The considerations and calculations presented hereinabove were appliedto the separation to two closely related substances, propane andisobutane and to the case of the separation of two substances chemicallyfar removed from each other, water and methanol.

EXAMPLE 1

Separation of propane and isobutane (isobaric processes). The examplechosen is that of the mixture of:

1 kg propane +1 kg isobutane, liquid at 40° C.

Propane is the component A and isobutane is the component B.

Flows are calculated from the liquid-vapor equilibrium curves for p=10bars.

The flows are represented in FIGS. 22a, 22b respectively for thecomponents A and B. In FIG. 22a, the liquid flow of A may be followedfrom the top of the column: the reflux m_(A) =0.7 is returned; a smallpart vaporizes between 26.3° C. and 40° C.; the flow passes at 0.66; itis then reinforced a 1 kg of the charge (1.66); while being vaporizedcompletely at from 40° C. to 67.3° C., it passes at 0; in the inversedirection, the vapor flow passes from 0° to 67.3° C., attains 1.66 ° at40° C., and 1.7° at 26.3° C.

In FIG. 22b, the reflux of B in the vapor stage, is emitted at thebottom of the column, 67.3° C. from 67.3° C. to 40° C., it is suppliedby a small vaporization of the liquid, which descends; it attains 0.66°at 40° C., then decreases to 0° at 26.3° C.; in the inverse direction,the liquid phase is formed from 26.3° C. to 40° C., passing from 0 to0.66 at 40° C., where it is reinforced by one unit of the charge (1.66);it then slightly decreases to attain 1.55 at the foot of the column.

In the knowledge of the evolution of the flows, the heat exchanged alongthe column may now be calculated, by integrating section by section,according to Equation (5) ##EQU17## together with the flux of entropypassing from the PAC to the column, according to Equation (6). ##EQU18##Taking Q_(col) in (2), δm_(A) is determined, then taking δm_(A) andΔS_(th) in (3), M'_(A) is determined; finally by inserting δm_(A),M'_(A) and Q_(col) in (4), the work w is obtained.

The following numerical values are obtained for the principal entities:

M_(A) (26.3° C.)=1.7 kg/s (flow exiting on top)

M_(A) L_(A) (26.3° C.)=497 kW (latent heat)

m_(A) (26.3° C.)=0.7 kg/s (reflux)

M'_(A) (67.3° C.)=0.64 kg/s

M_(B) (67.3° C.)=0.56 kg/s (reflux)

m_(B) L_(B) (67.3° C.)=143 kW (latent heat)

Q_(col) =400 kW.

The work of separation W is

W=46 kW.

The ratio Q/W, Q being the heat supplied by the PAC to the assembly ofthe depletion module+boiler of B", is designated by the abbreviationCoP. The following is found:

CoP=750/46:16.3.

EXAMPLE 2 Separation of methanol and water (isobaric process)

The example chosen is that of the mixture: 0.1 kg methanol (coponentA)+0.9 kg water (component B), liquid, at 92° C.

Flows are calculated from the liquid-vapor equilibrium curve and areshown respectively, in FIGS. 23a and 23b.

Calculations are effected as in Example 1.

The following values are found:

M_(A) (64.5° C.)=0.142 kg/s (flow exiting on top)

M_(A) L_(A) (64.5° C.)=159 kW (latent heat)

m_(A) (64.5° C.)=0.042 kg/s (reflux)

M'_(A) (100° C.)=0.236 kg/s

M_(B) (100° C.)=0.108 kg/s (reflux)

m_(B) L_(B) (100° C.)=244 kW (latent heat)

Q_(col) =-54.4 kW

W=27 kW (work of separation)

COP:476/27 =17.6.

Practical Application of an Isothermal Process

The process employed is of the general type represented in FIG. 4.

From the equilibrium curves, the vapor and liquid flows of A and B arecalculated by the following equations:

in the rectification module: ##EQU19## in the depletion module:##EQU20## the total work of the compressors is expressed by ##EQU21##

EXAMPLE 3 Separation of Butane and Propane

Propane=component A

Butane=component B

The temperature of the machine is 40° C., the extreme pressures are:

for x_(A) =, 5.25 bars

for x_(A) =1, 13.92 bars.

The pressure of the introductory stage (x_(A) =0.5) is p=10 bars.

Flows are calculated from equilibrium curves. Results are compiled inFIGS. 24a and 24b, which are part of the description.

Calculation of the work yields:

W=42 kW.

EXAMPLE 4 Separation of Methanol and Water

Methanol:component A.

Water:component B.

Composition: x_(A) =0.1, x_(B) =0.9.

Extreme pressures are:

x_(A=) 0

x_(A) =1

P₀ =0.4738 bar

P₁ =1.696 bar

P₁ /P₀ =3.6

pressure at the introductory stage P=0.65 bar.

The flows of methanol (m_(A)) and of water (m_(B)) evolve as indicatedin FIGS. 25a and 25b, which are part of the description.

The value of work is W=25 kW.

Calculations of a Conventional Column (comparison)

The calculations were effected by assuming that the number of plates isinfinite and that the products A and B are extracted in the pure state.The diagram in FIG. 26 illustrates the notations used. Molar values areused, with respect to the case where 1 mole per second issues at the topof the column. The notation adopted is as follows: ##EQU22## L_(n-1)=liquid retrogradation flowing from the plate of rank n-1. V_(n) =vaporflows ascending from the plate of rank n

m₀ =removal of liquid at the bottom of the column.

By writing the material balances and the heat balance, respectively forΣr (rectification module) and Σe (depletion module), the followingrelationships are obtained: ##EQU23##

Application to the Propane-Butane Sample

The butane-propane mixture is introduced in the column at 40° C.

For this temperature, the liquid-vapor equilibrium curve yields thefollowing values:

x_(A) =0.55 and y_(A) =0.752.

These values make possible the calculation of the enthalpies at thelevel of the feed plate:

h_(a1) =1.75 kW; H_(a1) =16.28 kW .

By plotting the points (x_(A), h_(a1)) and (y_(A), H_(a1)) on a diagramand drawing the straight line which connects them with each other, thefollowing may be read on the ordinate:

P=34 kW and P₀ =-38 kW.

From the value of P: ##EQU24## which is the mole fraction of A extractedat the top of the column. The m₀ moles of B extracted at the bottom ofthe column have the same mass as 0.433 mole of A, therefore:

m₀ =0.328

In the knowledge of the values of m₀, P₀ and the enthalpy h₀ of theliquid at the bottom of the column, the quantity of the heat supplied tothe reboiler may be calculated:

Q=14.43 kW.

for a charge of 19.1 g of A and 19.1 g of B. If the charge introducedper second in the column comprises 1 kg of propane and 1 kg of butane,the heat Q furnished to the reboiler is

Q=756 kW,

Application to the Methanol-Water Sample

With the charge introduced at a temperature of 92.2° C., thevapor-liquid equilibrium curve yields the values of:

x_(A) =0.06 and y_(A) =0.324

At the level of the feed plate, the enthalpies have the values of:

h_(a1) =2.11 kW and H_(a1) =40.55 kW

Following the procedure of the preceding example yields: ##EQU25##Q=465.6 kW which is the heat to be supplied to the reboiler for a chargeintroduced to the column per second, comprising 0.1 kg methanol and 0.9kg water.

The results of the abovementioned calculation are compiled in the tablehereinafter:

    ______________________________________                                                            Propane                                                                              Methanol                                                               i-butane                                                                             water                                              ______________________________________                                        Incident heat             40° C.                                                                          92.3° C.                            of mixture                                                                    Conventional column       756      465.6                                      heat supplied (kW)                                                            PAC POL* in assis-                                                                          W.sub.meca (kW)                                                                           91.1     44.4                                       tance to the conven-                                                                        COP          8.3     10.5                                       tional column                                                                 W.sub.meca reversible (for                                                                              46       27                                         isothermal or isobaric                                                        process)                                                                      COP of PAC POL*           16.3     17.6                                       with polytropic                                                               column (isobaric                                                              process                                                                       ______________________________________                                         *PAC POL = polytropic system wherein the vapor circulates in the directio     of rising temperatures and wherein the difference of the vapor and liquid     flows is zero.                                                           

According to the invention, the respective COP are:

propane-isobutane, COP=5

methanol-water, COP=6.5.

With respect to rectification in a conventional column, for which heatequivalent to 10 kW is supplied to the boiler, rectification byconventional column, combined with a conventional heat pump, requiresthe supply of mechanical work of 4 kW. According to the invention,rectification in a conventional column combined with a PAC POL consumes2 kW, while rectification by a polytropic column combined with a PAC POLconsumes only 1 kW. The advantages of the invention are thus clearlyapparent.

Among the polytropic processes according to the invention, preference isgiven to those employing the lowest number of mechanical components.From this point of view, the preferred processes are the isobaric andisothermal processes described in detail hereinabove. The isobaricsystem may contain a higher number of plates, but it is not necessary toprovide an exchanger per plate. It is possible to establish groups ofplates and combine a single exchanger with them, so that there will befewer exchangers along the column than plates.

In the case of the isothermal process, a compressor must be provided perplate.

If the substances to be separated are far removed from each other from achemical standpoint, such a process may be advantageous, because thenumber of plates is low. Furthermore, the temperature of the mixtureshould not be modified during rectification, which may be important inthe case of substances sensitive to temperature.

In a general manner, it is emphasized that the invention, to obtain thesame results as a conventional rectification process, employs a columncontaining fewer plates than the known method. Furthermore, to produce Aand B in identical quantities, the invention makes it possible to use acolumn with a smaller diameter.

Over all, the column according to the invention is thinner and containsfewer plates than the conventional rectifying columns.

It will be apparent to those skilled in the art that the presentinvention offers numerous possibilities concerning the rectification ofbinary mixtures.

What is claimed is
 1. In a process for the rectification of a mixturecomprised of components "A" and "B", wherein said mixture is fed to theintermediate state of a rectification column comprising in sequence adepletion stage, an intermediate stage, and a rectification stage, avapor stream and a liquid stream passing between said stages in acountercurrent manner with said vapor stream moving in a direction fromsaid depletion stage toward said rectification stage and said liquid,stream moving in a direction from said rectification stage toward saiddepletion stage, said vapor and liquid being in equilibrium in eachstage, component "A" being recovered as a vapor from said rectificationstage and component "B" being recovered as a liquid from said depletionstage, the temperature-pressure relationship in the column being suchthat substantially pure component "A" vapor is present in therectification stage and substantially pure component "B" liquid ispresent in the depletion stage, the improvement comprising:employing apolytropic process wherein rectification of the binary mixture of thetwo components A and B takes place without the external addition of heatand only work is provided, the latter being of a value close to thetheoretical value of the work necessary for the separation of thecomponents A and B, said polytropic process including the steps of: (a)partially condensing said recovered component "A" vapor; (b) passingsaid component "A" vapor in indirect heat exchange relationshipsequentially to said rectification, intermediate, and depletion stages,to provide said stages with an amount of heat adequate to achievethermodynamic equilibrium between the vapor and liquid phase of saidmixture, said component "A" vapor being compressed as it passes fromheat exchange relationship with one stage to heat exchange relationshipwith the next stage and being compressed as it passes from heat exchangerelationship with one stage to heat exchange relationship with the nextstage and being compressed subsequent to passing from heat exchangerelationship with said depletion stage, and thereafter cooling saidcomponent "A" vapor to provide a condensed component "A"; (c) recoveringa portion of said liquid component "B" as product and vaporizing theremainder of said component "B" liquid stream not recovered as productby use of the heat of condensation provided by the condensation of thecomponent "A" vapor and passing said vaporized component "B" to saiddepletion stage as reflux; (d) recovering a portion of said condensedcomponent "A" as product and passing the remainder of the condensedcomponent "A" in countercurrent direct mass and heat exchange andequilibrium relationship with said vaporized component "A" which passesin indirect heat exchange relationship with said stages; and, (e)feeding said condensed component "A" subsequent to passing in indirectheat exchange and equilibrium relationship with said vaporized component"A" to said rectification stage as reflux.
 2. The process of claim 1wherein said depletion and rectification stage each comprise multiplezones.
 3. The process of claim 1 wherein said liquid mixture which iscomprised of components A and B contains X amount of component A and Yamount of component B, said X amount of component A being recovered asproduct and said Y amount of component B being recovered as product.